Finite temperature oscillations of a Bose-Einstein condensate in a two-gasmodel

The temperature dependence of the frequencies of a Bose-Einstein condensate obtained in experiment has not been fully understood theoretically. In thi s paper we present a simplified version of a two-gas model. The ground stat e of the system found numerically is used for small oscillation analysis. I n the case of spherical symmetry a full spectrum of frequencies is found fo r low orbital quantum numbers. Avoided crossings that appear in the spectru m might be the reason for experimentally observed frequency shifts.